@article{JEDP_1989____A5_0, author = {Liess, Otto}, title = {Global existence for the nonlinear equations of crystal optics}, journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {5}, pages = {1--11}, publisher = {Ecole polytechnique}, year = {1989}, zbl = {0688.35091}, mrnumber = {1030820}, language = {en}, url = {http://www.numdam.org/item/JEDP_1989____A5_0/} }
Liess, Otto. Global existence for the nonlinear equations of crystal optics. Journées équations aux dérivées partielles (1989), article no. 5, 11 p. http://www.numdam.org/item/JEDP_1989____A5_0/
Calcul symbolic et propagation des singularités pour les équations aux derivées partielles non linéaires. Ann. Sc. E.N.S. 14 (1981), 209-246. | Numdam | MR | Zbl
[1] :Principles of optics, 3rd ed., Pergamon Press, 1964.
- [1] :Methoden der mathematischen Physik. vol. II, Springer Verlag, 1937, and revised English version in Interscience Publ., 1962. | JFM | Zbl
- [1] :Delayed singularity formation in solutions of nonllinear wave equations in higher dimension. Comm. Pure Appl. Math., 29 (1976), 649-681. | MR | Zbl
[1] :Lower bounds for the life span of solutions of nonlinear wave equations in three dimensions. Comm. Pure Appl. Math., 36 (1983), 1-35. | MR | Zbl
[2] :Almost global existence of elastic waves of finite amplitude arising from small initial disturbances. Comm. Pure Appl. Math., 41:3 (1988), 615-667. | MR | Zbl
[3] :The Cauchy problem for quasi-linear symmetric hyperbolic systems. Arch. Rat. Mech. Anal. 58 (1975), 181-205. | MR | Zbl
[1] :Global existence for nonlinear wave equations. Comm. Pure Appl. Math. 33 (1980), 43-101. | MR | Zbl
[1] :Long time behaviour of solutions to nonlinear wave equations. Proc. Int. Congress Math. at Warsaw 1983. 1209-1215. | MR | Zbl
[2] :Global small amplitude solutions to nonlinear evolution equations. Comm. Pure Appl. Math., 36, (1983), 133-141. | MR | Zbl
- [1] :Decay estimates for solutions of the system of crystal optics. To appear. | Zbl
[1] :Dispersion for nonlinear relativistic equations. Ann. E.N.S., 4e serie (1968), 459-497. | Numdam | MR | Zbl
[1] :Space time decay for solutions of wave equations. Advances in Math., 22 (1976), 305-311. | MR | Zbl
[2] :Global existence of small solutions to nonlinear evolution equations. J. diff. equations, 46 (1982), 409-425. | MR | Zbl
[1] :Vorlesungen über theoretische Physik, Bd. III u. IV, Akademische Verlagsgesellschaft, Leipzig, 1964.
[1] :Decay and asymptotics for □u = F(u). J. Funct. Anal. 2 (1968), 409-457. | MR | Zbl
[1]:Everywhere defined wave equations. in “Nonlinear evolution equations”, M.G. Crandall Ed., Academic Press, 1978, 85-102. | MR | Zbl
[2] :Convolution with kernels having singularities on a sphere. Trans. A.M.S., 148 (1970), 461-471. | MR | Zbl
[1] :A priori estimates for the wave equation and some applications. J. Funct. Analysis, 5 (1970), 218-235. | MR | Zbl
[2] :Pseudodifferential operators. Princeton University Press, Princeton, New Jersey, 1981. | MR | Zbl
[1] :Lp-decay rates for homogeneous wave equations. Math. Zeitschrift, 120 (1971), 93-106. | Zbl
[1] :Quantum electronics, second edition. John Wiley, Sons, Inc., New York - London - Sydney - Toronto, 1975.
[1] :